Internal problem ID [5759]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section A,
Drill exercises. Page 309
Problem number: 4(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-7 y^{\prime }+12 y-t \,{\mathrm e}^{2 t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(t),t$2)-7*diff(y(t),t)+12*y(t)=t*exp(2*t),y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{3 t} c_{2}+c_{1} {\mathrm e}^{4 t}+\frac {\left (2 t +3\right ) {\mathrm e}^{2 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 33
DSolve[y''[t]-7*y'[t]+12*y[t]==t*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} e^{2 t} \left (2 t+4 e^t \left (c_2 e^t+c_1\right )+3\right ) \\ \end{align*}